Preheat a 4-quart pot over medium heat and add the oil. Sauté the onion in the oil with a pinch of salt until softened, about 3 minutes. Add the garlic and sauté for 30 seconds or so, just until fragrant.
Add the broccoli, carrots, turmeric, remaining ½ teaspoon salt, and broth. Cover and bring to a boil. Once boiling, lower the heat to a simmer. Cook for about 10 minutes, until the carrots are very tender.
In the meantime, we'll make the cashew cream. Drain the cashews and place in a blender, along with the broth, miso, and nutritional yeast. Blend like crazy, until smooth. This can take anywhere from 1 to 5 minutes depending on your machine. Scrape down the sides with a rubber spatula every now and again to make sure you get everything.
When the carrots are tender, add the cashew mixture to the soup. Use an immersion blender to purée, so that only tiny bits of broccoli and carrot are visible. Keep the soup on low heat, partially covered, for about 10 minutes, until thickened, stirring occasionally.
Once thickened, add the lemon juice and pepper, taste for seasoning, and serve. It thickens even more as it cools, so you'll need to thin out leftovers—if there are any!
